Unformatted text preview: ve that the price
is decreasing at a rate of $1.50 per PortaBoy sold. (Said diﬀerently, you can sell one more
PortaBoy for every $1.50 drop in price.) 4. To determine the price which will move 150 PortaBoys, we ﬁnd p(150) = −1.5(150)+250 = 25.
That is, the price would have to be $25. 5. If the price of a PortaBoy were set at $150, we have p(x) = 150, or, −1.5x+250 = 150. Solving,
we get −1.5x = −100 or x = 66.6. This means you would be able to sell 66 PortaBoys a week
if the price were $150 per system. Not all real-world phenomena can be modeled using linear functions. Nevertheless, it is possible to
use the concept of slope to help analyze non-linear functions using the following:
Definition 2.3. Let f be a function deﬁned on the interval [a, b]. The average rate of change
of f over [a, b] is deﬁned as:
f (b) − f (a)
Geometrically, if we have the graph of y = f (x), the average rate of change over [a, b] is the slope of
the line which connects (a, f (a)) and (b, f (b)). This is called the sec...
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